Poker texas holdem combinations: tie or not tie?

In Texas Hold'em poker, there are some cases where a particular card, often called kicker, acts as a tiebreaker between players to determine who wins the pot, or if the pot has to be shared.

For some combinations such as three or four of a kind, there is no doubt: the kicker is the 5th card of the chosen combination, and determines the winner.

Example

Alice has 7 and 10
Bob has 7 and K
On the board are 7, 7, 2, 3, 4

In that case, both have a three of a kind. But because Bob has a king and Alice only a 10, he wins.

Most of poker websites explaining the rules clearly mention the role of the kicker applying to three of a kind and double pairs. But much fewer say something about colors, straights and full houses, and I found many contradicting answers. I also asked the question to some used online poker players and they also gave me contradicting answers.

I have tried to search for official tournament rules, but most of them only explain what happens with bad behaviors, bad deals, incorrect or confusing betting, showing cards when you shouldn't, acting when it's not your turn, etc. without mentioning subtleties about combinations at all.

To simplify my question, I will take three examples; I think it's better to start with examples before getting to the general answer if one exists. So, what's happening in the following 3 examples? Could you give a more generalized answer?

Example 1 - Flushes

Alice has 2♣ and 3♣
Bob has 4♣ and 5♣
On the board are 6♣, 8♣, 10♣, 2♥, 5♦

Contradicting answer 1: it's a tie, because the highest card included in the flush is the 10, which everybody chooses to include in their 5 showdown cards.
Contradicting answer 2: Bob wins, because he has the greatest private card that is part of the flush

Example 2 - Straight

Alice has 6 and K
Bob has 6 and J
On the board are 4, 5, 7, 8, 10

Contradicting answer 1: it's a tie, because the greatest card in the straight is the 8 for both Alice and Bob
Contradicting answer 2: Alice wins, because she owns an extra king, compared to the jack of Bob

Example 3 - Full house

Alice has 3 and 7
Bob has 3 and 6
On the board are 3, 3, 2, 2, 5

Contradicting answer 1: it's a tie, because one is supposed to choose only five cards to make a combination, and a full house is already five cards. There couldn't be any kicker, and thus their showdowns are strictly equals.
Contradicting answer 2: Alice wins because of her extra 7, compared to the 6 of Bob

Note: I'm unable to post next to you, so I edit my own post; strange not be able to answer to an answer.

Ok, So if I summarize what you are saying :

• In the flush case, Bob wins because at some point, their hand differs. Technically, I can continue comparing the highest private card to decide who wins. I had it correct.
• In the straight case, if the highest card of the straight is public, then it's technically always a tie, no matter what the players had as second private card (asuming that only one of the two cards was part of the straight).
• In a full house if both players have the same triplet and the same pair, it's always a tie, no matter what the players had as second private card (assuming again that only one of the two was part of the full house).

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Welcome to B&CG! – Pat Ludwig Jan 13 '13 at 1:29
The hand with cards of a same suit is called a flush. The original questions referred to matching colors; this is misleading because matching only colors (as opposed to suits) is not a valid hand in any standard poker game. – sitnaltax Jan 13 '13 at 19:49

The first thing to mention is definitely that there are no extra cards. Poker hands are evaluated with exactly five cards. Sometimes you use all five community cards as your best hand, in which case your pocket is useless (bluffing aside, of course). So strike that right away: if you can't beat your opponent with five cards, you've lost (or tied).

The next step is to evaluate the hands. It starts like this:

1. Does any single player have a straight flush? If yes, he is the winner.
2. Do multiple players have a straight flush? If yes, the winner is the one with the highest card. If multiple people share the highest card (obviously in a different suit) they split the pot. (Note: Royal flush is excluded because it's just a special straight flush that no one else can beat.)
3. Does any single player have 4 of a kind? If yes, he is the winner.
4. Do multiple players have 4 of a kind? If yes, the one with the highest 'set of 4' is the winner. If multiple players have the highest set of 4 (which is not achievable with a standard poker deck, but is with a double deck or community cards), the one with the highest kicker (highest card not in the set of 4) is the winner. If this card is the same, they split the pot.
5. Does any single player have a full house? If yes, he is the winner.
6. Do multiple players have full houses? If yes, then keeping in mind that a full house is a 3-set and a 2-set, the player with the highest 3-set wins the pot. If multiple players share the highest 3-set (which isn't possible without community cards like in hold 'em, or a double deck) then the player with the highest 2-set is the winner. If the 2-set and 3-set is the same, those players split the pot.
7. Does any single player have a flush? If yes, he is the winner.
8. Do multiple players have a flush? If yes, the player with a flush with the highest unique card is the winner. This hand is similar to 'high card' resolution, where each card is effectively a kicker. Note that a flush requires the same suit, not just color. While the colors used on the suit are red and black, two each, there's nothing to that connection. A club is no more similar to a spade than it is to a heart - only suit matters. The colors are red and black for historical purposes and so the same deck can be played for other games where that might matter.
9. Does any single player have a straight? If yes, he wins the pot.
10. Do multiple players have straights? If so, the player with the highest straight wins. (a-2-3-4-5 is the lowest straight, while 10-j-q-k-a is the highest straight.) If multiple players share the highest straight, they split the pot.
11. Does any single player have a 3 of a kind? If yes, he wins the pot.
12. Do multiple players have 3 of a kind? If yes, the player with the highest 3-set wins the pot. If multiple players have the highest 3-set, the player with the highest kicker wins the pot. If multiple players tie for highest 3-set and highest kicker, the player with the next highest kicker wins the pot. If the players tie for the highest 3-set, highest kicker, and highest second kicker, the players split the pot.
13. Does any single player have 2-pair? If yes, he wins the pot.
14. Do multiple players have 2-pair? If yes, the player with the highest pair wins the pot. If multiple players tie for the highest pair, the player with the second highest pair wins the pot. If multiple players tie for both pairs, the player with the highest kicker wins the pot. If multiple players tie for both pairs and the kicker, the players split the pot.
15. Does any single player have a pair? If yes, he wins the pot.
16. Do multiple players have a pair? If yes, the player with the highest pair win. If multiple players have the highest pair, the player with the highest kicker wins. Compare second and third kickers as expected to resolve conflicts, or split if all three kickers tie.
17. At this point, all cards are kickers, so compare the first, second, third, fourth, and if necessary, fifth highest cards in order until a winner is resolved, or split the pot if the hands are identical.
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Nothing can be more accurate and complete answer. Thank you very much ! – QuentinC Jan 13 '13 at 9:14
Where does this tell about five of a color, such as example 1 in the question? – b_jonas Jan 13 '13 at 19:26
1. You forgot flushes! 2. It's possible for multiple players to share the same 4-of-a-kind or 3-of-a-kind in single-deck games with shared cards, like Texas Hold'em. – sitnaltax Jan 13 '13 at 19:43
@user8067: There is no hand composed of five of a color. However, this answer omits five of a suit, which is a flush, and ranks above a straight and below a full house. – sitnaltax Jan 13 '13 at 19:50
@sitnaltax For sure, I thought I added the commnunity qualifier to that like I did to full house... looks like I omitted it. I wrote it pretty late :) – corsiKa Jan 14 '13 at 16:44

First of all: in your examples 2 and 3, the 'extra cards' (Alice's king and Bob's jack in example 2, and Alice's 7 and Bob's 6 in example 3) effectively don't exist: for comparison purposes, you use precisely each player's best 5-card hand. Those hands are 45678 in example 2 and 33322 in example 3; any additional cards in the player's hands are entirely moot.

Example 1, on the other hand, follows exactly the rules for kicker cards: Alice's flush is 2, 3, 6, 8, ten (of hearts), while Bob's is 4, 5, 6, 8, ten (of hearts). Since Bob's cards are 'higher' than Alice's, Bob wins the hand. More generically, what's used for flushes (and technically for straights) is lexicographic order : compare the highest cards (in the player's 5-card hands, remember!); if they're the same, compare the second-highest cards; and so on down to the end. As soon as you find one card higher than the other, that player wins; if you never find any cards higher than the other, then it's a tie. This is the idea that covers examples 2 and 3. (Technically it covers example 1, too - it's just that that example falls into the tie case.)

The same concept works for the other classes of hands too, but you have to be careful about comparison order; for pairs, two pairs, and three of a kinds, compare the 'feature' cards first (this is where kickers come into play, when the feature cards are the same: ten, ten, king, three, two beats ten, ten, queen, jack, nine, but king, king, 4, 3, 2 would beat queen, queen, jack, ten, 9). For full houses, always compare the three-of-a-kinds first (so a hand of 5, 5, 5, 4, 4 would still beat a hand of 3, 3, 3, King, King).

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protected by Community♦Sep 30 '14 at 17:40

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